[Nonlinearity is an important consideration in many problems of finance and economics, such as pricing securities and solving equilibrium models. This article provides analytical treatment of a general class of nonlinear transforms for processes with tractable conditional characteristic functions. We extend existing results on characteristic function-based transforms to a substantially wider class of nonlinear functions while maintaining low dimensionality by avoiding the need to compute the density function. We illustrate the applications of the generalized transform in pricing defaultable bonds with stochastic recovery. We also use the method to analytically solve a class of general equilibrium models with multiple goods and apply this model to study the effects of time-varying labor income risk on the equity premium.]

A buyer suggests prices to N sellers in a time period and buys from the seller who accepts the bid first. The number of bidding rounds is determined by how frequently the buyer can make an offer. We show that with no limit on the frequency and without discounting, the price path is either kept flat initially with large jumps at the end or increasing steadily over time. Which class of path occurs in equilibrium depends on the buyer's trade-off between committing to a price ceiling versus finely screening the sellers' costs. With discounting, limiting the number of rounds mitigates the delay caused by the reluctance to raise bids in the first class of equilibrium and therefore can benefit the buyer. This result suggests why, in reality, bargaining parties often take measures to make their offers rigid and consequently force themselves to make fewer offers.

[Risks of rare economic disasters can have a large impact on asset prices. At the same time, difficulties in inference regarding both the likelihood and severity of disasters, as well as agency problems, can lead to significant disagreements among investors about disaster risk. We show that such disagreements generate strong risk-sharing motives, such that just a small number of optimists in the economy will significantly reduce the disaster risk premium. Our model highlights the "latent" nature of disaster risk. The disaster risk premium will likely be low and smooth during normal times but increases dramatically when the risk-sharing capacity of the optimists is reduced, e.g., following a disaster. The model also helps reconcile the difference in the amount of disaster risk implied by financial markets and international macroeconomic data, and provides caution to the approach of extracting disaster probabilities from asset prices, which will disproportionately reflect the beliefs of a small group of optimists. Finally, our model predicts an inverse U-shaped relation between the equity premium and the size of the disaster insurance market.]

Nonlinearity is an important consideration in many problems of finance and economics, such as pricing securities and solving equilibrium models. This article provides analytical treatment of a general class of nonlinear transforms for processes with tractable conditional characteristic functions. We extend existing results on characteristic function-based transforms to a substantially wider class of nonlinear functions while maintaining low dimensionality by avoiding the need to compute the density function. We illustrate the applications of the generalized transform in pricing defaultable bonds with stochastic recovery. We also use the method to analytically solve a class of general equilibrium models with multiple goods and apply this model to study the effects of time-varying labor income risk on the equity premium.

Although the threat of rare economic disasters can have large effect on asset prices, difficulty in inference regarding both their likelihood and severity provides the potential for disagreements among investors. Such disagreements lead investors to insure each other against the types of disasters each one fears the most. Due to the highly nonlinear relationship between consumption losses in a disaster and the risk premium, a small amount of risk sharing can significantly attenuate the effect that disaster risk has on the equity premium. We characterize the sensitivity of risk premium to wealth distribution analytically. Our model shows that time variation in the wealth distribution and the amount of disagreement across agents can both lead to significant variation in disaster risk premium. It also highlights the conditions under which disaster risk premium will be large, namely when disagreement across agents is small or when the wealth distribution is highly concentrated in agents fearful of disasters. Finally, the model predicts an inverse U-shaped relationship between the equity premium and the size of the disaster insurance market.